Question: Simplify the following expression: $k = \dfrac{-20x^2 + 6x}{12x}$ You can assume $x \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-20x^2 + 6x = - (2\cdot2\cdot5 \cdot x \cdot x) + (2\cdot3 \cdot x)$ The denominator can be factored: $12x = (2\cdot2\cdot3 \cdot x)$ The greatest common factor of all the terms is $2x$ Factoring out $2x$ gives us: $k = \dfrac{(2x)(-10x + 3)}{(2x)(6)}$ Dividing both the numerator and denominator by $2x$ gives: $k = \dfrac{-10x + 3}{6}$